Zotero works with Google Docs! You must have the Zotero Connector installed in Chrome, Firefox or Safari.
Instead of a toolbar with buttons, as in Word, look for the Zotero menu in your Google Docs editor.
Just as with Word, your citations will be linked to Zotero, so if you change anything in a citation's entry in Zotero it will automatically update in Google Docs. To prompt it to do so, click "refresh."